
Signal to error ratio (SER):
\(\mathbf {SER} = 20\log _{10} {\frac{ \Vert \mathbf {x}_{\textrm { orig}}\Vert _2}{||\mathbf {x}_{\textrm {orig}}-\mathbf {x}_{\textrm {rec}}||_{2}}},\) 
where \(||\cdot ||_{2}\)  donates the \(\ell _{2}\)  norm, and \(\mathbf {x}_{orig}\)  and \(\mathbf {x}_{rec}\)  denote the original and the reconstructed images, respectively.

Peak Signal to Noise Ratio (PSNR):
\(\mathbf {PSNR} = 20\log _{10} {\frac{\max \lbrace \mathbf {x}_{\textrm { orig}}\rbrace }{||\mathbf {x}_{\textrm {orig}}-\mathbf {x}_{\textrm {rec}}||_{2}}}.\) 

Normalized High Frequency Error (HFEN) [1]}: This measures the quality of fine features, edges, and spatial blurring in the images and is defined as:
\(\mathbf {HFEN} = 20\log _{10} {\frac{||\textrm {LoG}(\mathbf {x}_{\textrm {orig}})-\textrm {LoG}(\mathbf {x}_{\textrm {rec} })||_{2}}{||\textrm {LoG}(\mathbf {x}_{\textrm {orig}})||_{2}} },\) 
where \(\textrm {LoG}\)  is a Laplacian of the Gaussian filter that captures edges. We use the same filter specifications as did Ravishankar et al. [1]}: kernel size of 15 \(\times \)  15 pixels, with a standard deviation of 1.5.

The Structural Similarity index (SSIM) is a perceptual metric introduced in [3]}, whose implementation is publicly available. We used the default contrast values, Gaussian kernel size of 11 \(\times \)  11 pixels with a standard deviation of 1.5 pixels.

BRISQUE is a referenceless measure of image quality, where a smaller score indicates better perceptual quality. BRISQUE estimates and gets the score using a support vector regression (SVR) model with the help of an image database and corresponding differential mean opinion score values. The distorted image database such as compression artifacts, blurring, and noise images, and with pristine versions of the distorted images [4]}.

